Average Error: 0.0 → 0.0
Time: 5.9s
Precision: 64
\[x \cdot y + z \cdot \left(1 - y\right)\]
↓
\[\mathsf{fma}\left(x, y, z \cdot \left(1 - y\right)\right)\]
x \cdot y + z \cdot \left(1 - y\right)
↓
\mathsf{fma}\left(x, y, z \cdot \left(1 - y\right)\right)
double f(double x, double y, double z) {
        double r600155 = x;
        double r600156 = y;
        double r600157 = r600155 * r600156;
        double r600158 = z;
        double r600159 = 1.0;
        double r600160 = r600159 - r600156;
        double r600161 = r600158 * r600160;
        double r600162 = r600157 + r600161;
        return r600162;
}
↓
double f(double x, double y, double z) {
        double r600163 = x;
        double r600164 = y;
        double r600165 = z;
        double r600166 = 1.0;
        double r600167 = r600166 - r600164;
        double r600168 = r600165 * r600167;
        double r600169 = fma(r600163, r600164, r600168);
        return r600169;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.0
Target0.0
Herbie0.0
\[z - \left(z - x\right) \cdot y\]

Derivation

  1. Initial program 0.0

    \[x \cdot y + z \cdot \left(1 - y\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(1 - y\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(1 - y\right)\right)\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (- z (* (- z x) y))

  (+ (* x y) (* z (- 1 y))))